caa a22 4500 445362162 CHVBK 20180317142918.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11071-010-9916-y doi (NATIONALLICENCE)springer-10.1007/s11071-010-9916-y Stabilization of fractional order systems using a finite number of state feedback laws [Elektronische Daten] [Saeed Balochian, Ali Sedigh, Mohammad Haeri] In this paper, the stabilization of linear time-invariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1<q<2. To this end, an extremum-seeking method is used for obtaining Lyapunov function and defining a suitable sliding sector in order to enable switching between available control gains for system stabilization. Consequently, using the LMI approach in fractional order systems, necessary and sufficient conditions are provided for stabilization of systems with fractional order 1<q<2 using a limited number of available state feedback gains which lead to variable structure control. Springer Science+Business Media B.V., 2010 Fractional order hybrid system nationallicence Linear matrix inequality (LMI) nationallicence Variable structure control nationallicence Balochian Saeed Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran aut Sedigh Ali Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran, Iran aut Haeri Mohammad Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran aut Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 141-152 0924-090X 66:1-2<141 2011 66 11071 https://doi.org/10.1007/s11071-010-9916-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9916-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balochian Saeed Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran aut NATIONALLICENCE 700 1- Sedigh Ali Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran, Iran aut NATIONALLICENCE 700 1- Haeri Mohammad Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 141-152 0924-090X 66:1-2<141 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer